Does anyone permit writing Shir HaShirim on klaf from a non-kosher species?

Question

A Torah, tefillin, mezuzah, and Esther scroll must be written on klaf that comes from a kosher species. See Shulchan Aruch OH 32:12 (and OH 691:1 and YD 271:1):

יהיה הקלף מעור בהמה חיה ועוף ידהטהורים

The parchment must be [made] from the skin of a domesticated animal, wild animal, or bird which are kosher

The Magen Avraham writes that this is the case for other books that contain names of God that may not be erased (sheimot):

‮בתו' סוטה דף י"ז ע"ב כתבו בשם הירושלמי דאפילו שאר ספרים שיש בהם שמות אסור לכתוב על עור בהמה טמאה.

The Tosafot on Sota 17b write in the name of the Yerushalmi that it is even forbidden to write other sefarim that contain sheimot on skin of a non-kosher animal.

The Mishnah Berurah on OH 32 in Biur Halacha s.v. תורת ה׳ writes that books (like the Gemara) containing allusions (רמזים, remezim) to God but no actual sheimot may be written on klaf from a non-kosher animal.

Where do kinnuyim (כינויים, nicknames) of God fall in this hierarchy? For example, the book of Shir HaShirim does not contain any sheimot (unless I missed something!), but it does contain kinnuyim: almost all occurrences of "Shlomo" are such (see eg. Rambam MT Yesodei HaTorah 6:9, h/t DoubleAA).

Does anyone discuss my general question, or the specific question of whether Shir HaShirim may be written on klaf from a non-kosher animal? For Shir HaShirim, if it is permitted, would it have the same holiness as if it were written on klaf from a kosher animal?

Answer 1

The Biur Halacha's words are:

ואפילו שאר ספרים שאינם תנ"ך שיש בהם שמות שאינם נמחקים אסור לכתוב על עור בהמה טמאה

So it is clear that any sefer of Tanach cannot be written on klaf from a non-kosher animal. The reason is that by being part of Tanach it automatically has holiness even without names of G-d. So Shir HaShirim and Megillas Esther would be included. The Biur Halacha is adding that even books without the holiness of Tanach must be written on kosher animal klaf if they have names of G-d.